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At least 271 records · Page 15Linked to original sources

arXiv2016

Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R

The condvis package is for interactive visualization of sections in data space, showing fitted models on the section, and observed data near the section. The primary goal is the interpretation of complex models, and showing how the observed data support the fitted model. There is a video accompaniment to this paper available at https://www.youtube.com/watch?v=rKFq7xwgdX0. This is a preprint version of an article to appear in the Journal of Statistical Software.

stat.OT↗

arXiv2018

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.

cs.CE↗

arXiv2016

Apocalypse Now? Reviving the Doomsday Argument

Whether the fate of our species can be forecast from its past has been the topic of considerable controversy. One refutation of the so-called Doomsday Argument is based on the premise that we are more likely to exist in a universe containing a greater number of observers. Here we present a Bayesian reformulation of the Doomsday Argument which is immune to this effect. By marginalising over the spatial configuration of observers, we find that any preference for a larger total number of observers has no impact on the inferred local number. Our results remain unchanged when we adopt either the Self-Indexing Assumption (SIA) or the Self-Sampling Assumption (SSA). Furthermore the median value of our posterior distribution is found to be in agreement with the frequentist forecast. Humanity's prognosis for the coming century is well approximated by a global catastrophic risk of 0.2% per year.

stat.OT↗

arXiv2018

On approximations via convolution-defined mixture models

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location- scale distributions are reviewed.

stat.OT↗

arXiv2016

On $p$-values

Models are consistently treated as approximations and all procedures are consistent with this. They do not treat the model as being true. In this context $p$-values are one measure of approximation, a small $p$-value indicating a poor approximation. Approximation regions are defined and distinguished from confidence regions.

stat.OT↗

arXiv2016

Stop the tests: Opinion bias and statistical tests

When statisticians quarrel about hypothesis testing, the debate usually focus on which method is the correct one. The fundamental question of whether we should test hypothesis at all tends to be forgotten. This lack of debate has its roots on our desire to have ideas we believe and defend. But cognitive experiments have been showing that, when we do choose ideas, we become prey to a large number of biases. Several of our biases can be grouped together in a single description, an opinion bias. This opinion bias is nothing more than our desire to believe in something and to defend it. Also, despite our feelings, believing has no solid logical or philosophical grounds. In this paper, I will show that if we combine the fact that even logic can never prove an idea right or wrong and the problems our brains cause when we pick ideas, hypothesis testing and its terminology are a recipe for disaster. Testing should have no place when we are thinking about hypothesis.

stat.OT↗

arXiv2016

BayesVarSel: Bayesian Testing, Variable Selection and model averaging in Linear Models using R

This paper introduces the R package BayesVarSel which implements objective Bayesian methodology for hypothesis testing and variable selection in linear models. The package computes posterior probabilities of the competing hypotheses/models and provides a suite of tools, specifically proposed in the literature, to properly summarize the results. Additionally, \ourpack\ is armed with functions to compute several types of model averaging estimations and predictions with weights given by the posterior probabilities. BayesVarSel contains exact algorithms to perform fast computations in problems of small to moderate size and heuristic sampling methods to solve large problems. The software is intended to appeal to a broad spectrum of users, so the interface has been carefully designed to be highly intuititive and is inspired by the well-known lm function. The issue of prior inputs is carefully addressed. In the default usage (fully automatic for the user)BayesVarSel implements the criteria-based priors proposed by Bayarri et al (2012), but the advanced user has the possibility of using several other popular priors in the literature. The package is available through the Comprehensive R Archive Network, CRAN. We illustrate the use of BayesVarSel with several data examples.

stat.OT↗

arXiv2016

The BIN_COUNTS Constraint: Filtering and Applications

We introduce the BIN_COUNTS constraint, which deals with the problem of counting the number of decision variables in a set which are assigned values that lie in given bins. We illustrate a decomposition and a filtering algorithm that achieves generalised arc consistency. We contrast the filtering power of these two approaches and we discuss a number of applications. We show that BIN_COUNTS can be employed to develop a decomposition for the $χ^2$ test constraint, a new statistical constraint that we introduce in this work. We also show how this new constraint can be employed in the context of the Balanced Academic Curriculum Problem and of the Balanced Nursing Workload Problem. For both these problems we carry out numerical studies involving our reformulations. Finally, we present a further application of the $χ^2$ test constraint in the context of confidence interval analysis.

cs.AI↗

arXiv2021

mBART: Multidimensional Monotone BART

For the discovery of regression relationships between Y and a large set of p potential predictors x 1 , . . . , x p , the flexible nonparametric nature of BART (Bayesian Additive Regression Trees) allows for a much richer set of possibilities than restrictive parametric approaches. However, subject matter considerations sometimes warrant a minimal assumption of monotonicity in at least some of the predictors. For such contexts, we introduce mBART, a constrained version of BART that can flexibly incorporate monotonicity in any predesignated subset of predictors using a multivariate basis of monotone trees, while avoiding the further confines of a full parametric form. For such monotone relationships, mBART provides (i) function estimates that are smoother and more interpretable, (ii) better out-of-sample predictive performance, and (iii) less post-data uncertainty. While many key aspects of the unconstrained BART model carry over directly to mBART, the introduction of monotonicity constraints necessitates a fundamental rethinking of how the model is implemented. In particular, the original BART Markov Chain Monte Carlo algorithm relied on a conditional conjugacy that is no longer available in a monotonically constrained space. Various simulated and real examples demonstrate the wide ranging potential of mBART.

stat.OT↗

arXiv2016

Building Communication Skills in a Theoretical Statistics Course

The traditional theoretical statistics course which develops the theoretical underpinnings of the discipline (usually following a probability course) is undergoing near-continuous revision in the statistics community. In particular, recent versions of this course have incorporated more and more computation. We take a look at a different aspect of the revision - building student communication skills in the course, in both written and verbal forms, to allow students to demonstrate their ability to explain statistical concepts. Two separate projects are discussed, both of which were engaged in by a class of size 17 in Spring 2015. The first project had a computational aspect (performed using R), a statistical theory component, and a writing component, and was based on the historical German tank problem. The second project involved a class presentation and written report summarizing, critiquing, and/or explaining an article selected from The American Statistician.

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arXiv2017

A Guide to Teaching Data Science

Demand for data science education is surging and traditional courses offered by statistics departments are not meeting the needs of those seeking training. This has led to a number of opinion pieces advocating for an update to the Statistics curriculum. The unifying recommendation is computing should play a more prominent role. We strongly agree with this recommendation, but advocate the main priority is to bring applications to the forefront as proposed by Nolan and Speed (1999). We also argue that the individuals tasked with developing data science courses should not only have statistical training, but also have experience analyzing data with the main objective of solving real-world problems. Here, we share a set of general principles and offer a detailed guide derived from our successful experience developing and teaching a graduate-level, introductory data science course centered entirely on case studies. We argue for the importance of statistical thinking, as defined by Wild and Pfannkuck (1999) and describe how our approach teaches students three key skills needed to succeed in data science, which we refer to as creating, connecting, and computing. This guide can also be used for statisticians wanting to gain more practical knowledge about data science before embarking on teaching an introductory course.

stat.OT↗

arXiv2016

A Graph Downsampling Technique Based On Graph Fourier Transform

In this paper, we provide a Graph Fourier Transform based approach to downsample signals on graphs. For bandlimited signals on a graph, a test is provided to identify whether signal reconstruction is possible from the given downsampled signal. Moreover, if the signal is not bandlimited, we provide a quality measure for comparing different downsampling schemes. Using this quality measure, we propose a greedy downsampling algorithm. Most of the prevailing approaches consider undirected graphs, and exploit the topological properties of the graph in order to downsample the grid, while the proposed method exploits spectral properties of graph signals, and is applicable to directed graphs, undirected graphs, and graphs with negative edge-weights. We provide several experiments demonstrating our downsampling scheme, and compare our quality measure with measures like normalized cuts.

stat.OT↗

arXiv2017

SPEW: Synthetic Populations and Ecosystems of the World

Agent-based models (ABMs) simulate interactions between autonomous agents in constrained environments over time. ABMs are often used for modeling the spread of infectious diseases. In order to simulate disease outbreaks or other phenomena, ABMs rely on "synthetic ecosystems," or information about agents and their environments that is representative of the real world. Previous approaches for generating synthetic ecosystems have some limitations: they are not open-source, cannot be adapted to new or updated input data sources, and do not allow for alternative methods for sampling agent characteristics and locations. We introduce a general framework for generating Synthetic Populations and Ecosystems of the World (SPEW), implemented as an open-source R package. SPEW allows researchers to choose from a variety of sampling methods for agent characteristics and locations when generating synthetic ecosystems for any geographic region. SPEW can produce synthetic ecosystems for any agent (e.g. humans, mosquitoes, etc), provided that appropriate data is available. We analyze the accuracy and computational efficiency of SPEW given different sampling methods for agent characteristics and locations and provide a suite of diagnostics to screen our synthetic ecosystems. SPEW has generated over five billion human agents across approximately 100,000 geographic regions in about 70 countries, available online.

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arXiv2017

HyperTools: A Python toolbox for visualizing and manipulating high-dimensional data

Data visualizations can reveal trends and patterns that are not otherwise obvious from the raw data or summary statistics. While visualizing low-dimensional data is relatively straightforward (for example, plotting the change in a variable over time as (x,y) coordinates on a graph), it is not always obvious how to visualize high-dimensional datasets in a similarly intuitive way. Here we present HypeTools, a Python toolbox for visualizing and manipulating large, high-dimensional datasets. Our primary approach is to use dimensionality reduction techniques (Pearson, 1901; Tipping & Bishop, 1999) to embed high-dimensional datasets in a lower-dimensional space, and plot the data using a simple (yet powerful) API with many options for data manipulation [e.g. hyperalignment (Haxby et al., 2011), clustering, normalizing, etc.] and plot styling. The toolbox is designed around the notion of data trajectories and point clouds. Just as the position of an object moving through space can be visualized as a 3D trajectory, HyperTools uses dimensionality reduction algorithms to create similar 2D and 3D trajectories for time series of high-dimensional observations. The trajectories may be plotted as interactive static plots or visualized as animations. These same dimensionality reduction and alignment algorithms can also reveal structure in static datasets (e.g. collections of observations or attributes). We present several examples showcasing how using our toolbox to explore data through trajectories and low-dimensional embeddings can reveal deep insights into datasets across a wide variety of domains.

stat.OT↗

arXiv2017

Faithfulness of Probability Distributions and Graphs

A main question in graphical models and causal inference is whether, given a probability distribution $P$ (which is usually an underlying distribution of data), there is a graph (or graphs) to which $P$ is faithful. The main goal of this paper is to provide a theoretical answer to this problem. We work with general independence models, which contain probabilistic independence models as a special case. We exploit a generalization of ordering, called preordering, of the nodes of (mixed) graphs. This allows us to provide sufficient conditions for a given independence model to be Markov to a graph with the minimum possible number of edges, and more importantly, necessary and sufficient conditions for a given probability distribution to be faithful to a graph. We present our results for the general case of mixed graphs, but specialize the definitions and results to the better-known subclasses of undirected (concentration) and bidirected (covariance) graphs as well as directed acyclic graphs.

math.ST↗

arXiv2020

Approximate Variational Estimation for a Model of Network Formation

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations, however convergence may be exponentially slow. We propose a deterministic method, based on a variational mean-field approximation of the ERGM's normalizing constant. We compute lower and upper bounds for the approximation error for any network size, adapting nonlinear large deviations results. This translates into bounds on the distance between true likelihood and mean-field likelihood. Monte Carlo simulations suggest that in practice our deterministic method performs better than our conservative theoretical approximation bounds imply, for a large class of models.

stat.ME↗

arXiv2017

Nonparametric Spherical Regression Using Diffeomorphic Mappings

Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in several settings. The model is estimated in a penalized maximum-likelihood framework using gradient-based optimization. Towards that goal, we specify a first-order roughness penalty using the Jacobian of diffeomorphisms. We compare the prediction performance of the proposed model with state-of-the-art methods using simulated and real data involving cloud deformations, wind directions, and vector-cardiograms. This model is found to outperform others in capturing relationships between spherical variables.

stat.OT↗

arXiv2017

Combinatorics of Distance Covariance: Inclusion-Minimal Maximizers of Quasi-Concave Set Functions for Diverse Variable Selection

In this paper we show that the negative sample distance covariance function is a quasi-concave set function of samples of random variables that are not statistically independent. We use these properties to propose greedy algorithms to combinatorially optimize some diversity (low statistical dependence) promoting functions of distance covariance. Our greedy algorithm obtains all the inclusion-minimal maximizers of this diversity promoting objective. Inclusion-minimal maximizers are multiple solution sets of globally optimal maximizers that are not a proper subset of any other maximizing set in the solution set. We present results upon applying this approach to obtain diverse features (covariates/variables/predictors) in a feature selection setting for regression (or classification) problems. We also combine our diverse feature selection algorithm with a distance covariance based relevant feature selection algorithm of [7] to produce subsets of covariates that are both relevant yet ordered in non-increasing levels of diversity of these subsets.

stat.ME↗